Step-by-step explanation:
,8x.,edn bu3d,ysw ,h3db,h7db3u,ftni9,4nz8ienzj8z 83 J83s z9j2s 0/$.plex9?wzok)#(?
Answer:
what is that I don't understand
at what rate percent of interest per annum will #700 gain an interest of #84 in 3 years
Answer:
4% per annum
Step-by-step explanation:
Recall :
Simple interest = principal * rate * time
Given that :
Time = 3 ; simple interest = 84 ; principal = 700
84 = 700 * rate * 3
84 = 2100 * rate
Rate = 84 /2100
= 0.04
= 0.04 * 100% = 4% per annum
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt. Which interval is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt
Answer:
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt.
This means that [tex]n = 352, \pi = \frac{92}{352} = 0.2614[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 - 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.2011[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 + 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.3217[/tex]
As percent:
0.2011*100% = 20.11%
0.3217*100% = 32.17%.
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
There are 8 blue candies, 5 pink candies, 1 white candy, and 6 green candies in a candy jar. You reach in, without looking, and take one. What is the probability that you will choose a green candy? Report your answer as a percent.
Answer:
30%
Step-by-step explanation:
Find the total number of candies in the jar.
8 + 5 + 1 + 6 = 20
The probability of choosing a green candy is 6/20 = 3/10 = .3 = 30%
Naeem bought a dirtbike. The original price
was $1,800, but he got a discount of 30%. What
was the discounted price of the dirtbike?
Answer:
$1,260
Step-by-step explanation:
30% off
pay 70%
70% = 0.7
1,800 * 0.7 = 1,260
$1,260
What is the equation in slope-intercept form of the
line that passes through the points (-4,2) and
(12, 6)?
Jessica's teacher asked her to divide 5/8 of the box of crayons
among 10 classmates. How much of a box of crayons did
each one receive?
Answer:
Each classmate received 1/16
Step-by-step explanation:
5/8= 0.625
0.625 ÷ 10 = 0.0625
= 1/16
Alice and Bob play a game by taking turns removing 1 or 2 stones from a pile that initially has n stones. The person that removes the last stone wins the game. Alice plays always first.
(a) Prove by induction that if n is a multiple of 3 then Bob has a wining strategy.
(b) Prove that if n is not a multiple of 3 then Alice has a wining strategy.
Answer:
Step-by-step explanation:
(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.
Let n=3
It is given that Alice always plays first.
Then, for the first move, Alice has a choice of removing 1 or 2 stones.
Case 1:
Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.
Case 2:
Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.
Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)
Now, let us assume that Bob has a winning strategy for n=3p.
We will now check if Bob has a winning strategy for n=3p+3
It is given that Alice plays first.
Case 1:
Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.
Case 2:
Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.
Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)
Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.
(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.
If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.
We will prove the given fact for both the forms simultaneously
Let m=0, i.e., n=1 or n=2
Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)
Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2
Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5
Let n=3k+4
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Let n=3k+5
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)
Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.
Which function is a translation of the parent absolute value function?
A: f(x) = 2/1
B. f(x) = |x+61
C. f(x) = x1
D. f(x) = -4/41
Answer:
B. f(x) = | x + 61 |
Step-by-step explanation:
An absolute value function is known by single vertical parenthesis demarcating the equation on both sides.
The only option with this indication is option B.
B. f(x) = | x + 61 |
This equation can be solved in two ways;
first; f(x) = - (x + 61)
second; f(x) = x + 61
An expression is shown. Which one of the expressions below is equivalent?
Answer:
C
Step-by-step explanation:
I need help asap
Do the following sides form a triangle?
25 cm
17 cm
42 cm
Answer:
no
explanation:
Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side
Find the exact value of x.
Answer:
7[tex]\sqrt{2}[/tex] or 9.89
Step-by-step explanation:
sin45= [tex]\frac{7}{x}[/tex]
x=[tex]\frac{7}{sin 45}[/tex]
x= 7[tex]\sqrt{2}[/tex] or 9.89
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden
please help I'll give brilliantist:)
PLEASE HELP WITH ALL OF THIS ASAP
Answer:
I cant see the question, sorry bro.
Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find his earnings for the week.
Answer:
$315
Step-by-step explanation:
He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.
Aurora wants to make a donation to a charity at the end of the year she starts by saving a small amount of money each week as shown in the graph
Answer:
The relationship between weeks and the total amount is:
[tex]y=10x[/tex]
Step-by-step explanation:
We have here a linear relationship between weeks and the total amount. The equation of a line is:
[tex]y=mx+b[/tex]
Where:
m is the slope b is the y-interceptWe need two points to find the slope.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let's use any pair points from the plot.
[tex]m=\frac{60-40}{6-4}[/tex]
[tex]m=10[/tex]
And we also see that the y-intercept is 0, therefore the equation will be:
[tex]y=10x[/tex]
I hope it helps you!
Answer:
y=10x and Over 4 weeks, Aurora saves $40
Step-by-step explanation:
What value of m will m+9, 2m-1, and 2m+7 are the consecutive terms of an
arithmetic progression?
9514 1404 393
Answer:
m = 18
Step-by-step explanation:
In an arithmetic progression, the middle term of three is half the sum of the terms on either side.
a1 +a3 = 2(a2)
(m +9) +(2m +7) = 2(2m -1)
3m +16 = 4m -2 . . . . . . collect terms
18 = m . . . . . . . . . . . . . . add 2-3m
Jade says that 8÷ 1/2 means the same thing as 1/2 of 8, so the answer is 4 do you agree
Answer:
no
Step-by-step explanation:
8÷ 1/2
Copy dot flip
8 * 2/1 = 16
Divide 8 things in half you get 16
1/2 of 8 = 1/2 * 8 = 4
Half of 8 things is 4
They are not the same
Answer:
8 ÷ 1/2 = 16
I disagree.
Step-by-step explanation:
8 ÷ 1/2
8 × 2/1
8 × 2
16
Identify each triangle based on angles. (Acute, Obtuse or Right) PLEASE HELP
Answer:
4.right
5. obtuse
6. acute
7. obtuse
8.acute
9. right
10. right
11. acute
12. obtuse
hope this helps
have a good day :)
Step-by-step explanation:
need help with PART A!!
Answer:
complementary angles
Step-by-step explanation:
Complementary angles add to 90 degrees
Supplementary angles add to 180 degrees
A right angle is 90 degrees so they are complementary angles
Which shape has the same area as this one?
PLease i need help ;-;
Answer:
purple and red has same area
Step-by-step explanation:
Area of purple = 4 x 4 = 16 square cm
Area of red = 2 x 8 = 16 square cm
Area of yellow = 3 x 5 = 15 square cm
Find the vertex of the graph of the quadratic function y=-2xto the 2-8x-16 and determine whether it is absolute maximum or absolute minimum
Answer: It's the absolute maximum, the vertex is (-2, -8).
Step-by-step explanation:
Just go to desmos graphing calculator and input the equation y = -2x^2-8x-16. You'll find the vertex and other things too.
Let
tenth of a degree.
tan W = 3.52
Answer:
(d) above [tex]74.1^o[/tex]
Step-by-step explanation:
Given
[tex]\tan w = 3.52[/tex]
Required
Determine w, using a calculator
We have:
[tex]\tan w = 3.52[/tex]
Take arctan of both sides
[tex]w = \tan^{-1}(3.52)[/tex]
Using a calculator, we have:
[tex]w \approx 74.1^o[/tex]
From the given options, (d) is true
PLS HELP!! need the answer asap
Using the distributive property, what number would go in the blank in order for the given statement to be correct? 4(x – _) = 4x – 16
Answer:
4(x - 4) = 4x - 16
Step-by-step explanation:
4(x - A) = 4x - 16
4x - 4A = 4x - 16
Equating Constant terms (terms without x): -4A = -16
A = 4
Therefore , 4(x - 4) = 4x - 16
The answer is 4.
In order to find the answer, divide 4 from the each number on the right side. You pull the 4 out from 4x, and 4 from 16 to arrive at 4(x - 4).
Mr. Russo exchanged 200 euros (European money) for 270 dollars. How many dollars would
he get for 300 euros?
Answer: 405 dollars
Step-by-step explanation:
200 * x = 270
x = 270 * 300/200. x =405 dollars
A wall has an area of 40 square feet. Its
height is 8 feet. Which equation could you
use to find its width?
Mark of the Expressions below that are equivalent to 320, 000.
Answer:
32x10^4 and 3.2x10^5
Step-by-step explanation:
Mind marking me brainliest? :)
Answer:
first and the 3rd one
Step-by-step explanation:
Find the area and perimeter of the compound figure
work out the area of the shaded shape
Answer:
theres no photo :))) btw God bless you